4.68/1.90 YES 4.80/1.92 proof of /export/starexec/sandbox/benchmark/theBenchmark.c 4.80/1.92 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 4.80/1.92 4.80/1.92 4.80/1.92 Termination of the given C Problem could be proven: 4.80/1.92 4.80/1.92 (0) C Problem 4.80/1.92 (1) CToIRSProof [EQUIVALENT, 0 ms] 4.80/1.92 (2) IntTRS 4.80/1.92 (3) TerminationGraphProcessor [SOUND, 46 ms] 4.80/1.92 (4) IntTRS 4.80/1.92 (5) IntTRSCompressionProof [EQUIVALENT, 0 ms] 4.80/1.92 (6) IntTRS 4.80/1.92 (7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] 4.80/1.92 (8) IntTRS 4.80/1.92 (9) PolynomialOrderProcessor [EQUIVALENT, 8 ms] 4.80/1.92 (10) YES 4.80/1.92 4.80/1.92 4.80/1.92 ---------------------------------------- 4.80/1.92 4.80/1.92 (0) 4.80/1.92 Obligation: 4.80/1.92 c file /export/starexec/sandbox/benchmark/theBenchmark.c 4.80/1.92 ---------------------------------------- 4.80/1.92 4.80/1.92 (1) CToIRSProof (EQUIVALENT) 4.80/1.92 Parsed C Integer Program as IRS. 4.80/1.92 ---------------------------------------- 4.80/1.92 4.80/1.92 (2) 4.80/1.92 Obligation: 4.80/1.92 Rules: 4.80/1.92 f1(c, x, y) -> f2(c, x_1, y) :|: TRUE 4.80/1.92 f2(x1, x2, x3) -> f3(x1, x2, x4) :|: TRUE 4.80/1.92 f3(x5, x6, x7) -> f4(0, x6, x7) :|: TRUE 4.80/1.92 f5(x8, x9, x10) -> f6(x8, arith, x10) :|: TRUE && arith = x9 - 1 4.80/1.92 f6(x26, x27, x28) -> f7(x26, x27, x29) :|: TRUE && x29 = x28 - 1 4.80/1.92 f7(x30, x31, x32) -> f8(x33, x31, x32) :|: TRUE && x33 = x30 + 1 4.80/1.92 f4(x17, x18, x19) -> f5(x17, x18, x19) :|: x18 > 0 && x19 > 0 4.80/1.92 f8(x20, x21, x22) -> f4(x20, x21, x22) :|: TRUE 4.80/1.92 f4(x23, x24, x25) -> f9(x23, x24, x25) :|: x24 <= 0 4.80/1.92 f4(x34, x35, x36) -> f9(x34, x35, x36) :|: x36 <= 0 4.80/1.92 Start term: f1(c, x, y) 4.80/1.92 4.80/1.92 ---------------------------------------- 4.80/1.92 4.80/1.92 (3) TerminationGraphProcessor (SOUND) 4.80/1.92 Constructed the termination graph and obtained one non-trivial SCC. 4.80/1.92 4.80/1.92 ---------------------------------------- 4.80/1.92 4.80/1.92 (4) 4.80/1.92 Obligation: 4.80/1.92 Rules: 4.80/1.92 f4(x17, x18, x19) -> f5(x17, x18, x19) :|: x18 > 0 && x19 > 0 4.80/1.92 f8(x20, x21, x22) -> f4(x20, x21, x22) :|: TRUE 4.80/1.92 f7(x30, x31, x32) -> f8(x33, x31, x32) :|: TRUE && x33 = x30 + 1 4.80/1.92 f6(x26, x27, x28) -> f7(x26, x27, x29) :|: TRUE && x29 = x28 - 1 4.80/1.92 f5(x8, x9, x10) -> f6(x8, arith, x10) :|: TRUE && arith = x9 - 1 4.80/1.92 4.80/1.92 ---------------------------------------- 4.80/1.92 4.80/1.92 (5) IntTRSCompressionProof (EQUIVALENT) 4.80/1.92 Compressed rules. 4.80/1.92 ---------------------------------------- 4.80/1.92 4.80/1.92 (6) 4.80/1.92 Obligation: 4.80/1.92 Rules: 4.80/1.92 f6(x26:0, x27:0, x28:0) -> f6(x26:0 + 1, x27:0 - 1, x28:0 - 1) :|: x27:0 > 0 && x28:0 > 1 4.80/1.92 4.80/1.92 ---------------------------------------- 4.80/1.92 4.80/1.92 (7) IntTRSUnneededArgumentFilterProof (EQUIVALENT) 4.80/1.92 Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: 4.80/1.92 4.80/1.92 f6(x1, x2, x3) -> f6(x2, x3) 4.80/1.92 4.80/1.92 ---------------------------------------- 4.80/1.92 4.80/1.92 (8) 4.80/1.92 Obligation: 4.80/1.92 Rules: 4.80/1.92 f6(x27:0, x28:0) -> f6(x27:0 - 1, x28:0 - 1) :|: x27:0 > 0 && x28:0 > 1 4.80/1.92 4.80/1.92 ---------------------------------------- 4.80/1.92 4.80/1.92 (9) PolynomialOrderProcessor (EQUIVALENT) 4.80/1.92 Found the following polynomial interpretation: 4.80/1.92 [f6(x, x1)] = x1 4.80/1.92 4.80/1.92 The following rules are decreasing: 4.80/1.92 f6(x27:0, x28:0) -> f6(x27:0 - 1, x28:0 - 1) :|: x27:0 > 0 && x28:0 > 1 4.80/1.92 The following rules are bounded: 4.80/1.92 f6(x27:0, x28:0) -> f6(x27:0 - 1, x28:0 - 1) :|: x27:0 > 0 && x28:0 > 1 4.80/1.92 4.80/1.92 ---------------------------------------- 4.80/1.92 4.80/1.92 (10) 4.80/1.92 YES 4.83/1.93 EOF